35x^3-28x^2=7x

Solution for 35x^3-28x^2=7x equation:

Simplifying
35x3 + -28x2 = 7x

Reorder the terms:
-28x2 + 35x3 = 7x

Solving
-28x2 + 35x3 = 7x

Solving for variable 'x'.

Reorder the terms:
-7x + -28x2 + 35x3 = 7x + -7x

Combine like terms: 7x + -7x = 0
-7x + -28x2 + 35x3 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-1 + -4x + 5x2) = 0

Factor a trinomial.
7x((-1 + -5x)(1 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -0.2, 1}